Here is a minor typing error:
Lemma 7 If T1 is
faithfully interpretable in T2 and T2 is faithfully interpretable in T2,
then T1 is faithfully
interpretable in T3.
I think you mean the bold red T2 to be
T3.
-Rich
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Michael Gruninger
Sent: Wednesday, December 14, 2011 7:32 AM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Ontology, Analogies and Mapping Disparate Fields
Hi Ali,
here is the submitted version of the modularity paper.
You can put it up on your own url somewhere until it
is
accepted by Applied Ontology.
- michael
Quoting Ali SH <asaegyn+out@xxxxxxxxx>:
> Hi all,
>
> Just wanted to pass along a link to an ontology
related story (though it's
> barely framed as such) in a relatively mainstream
technology news outlet:
> http://www.physorg.com/news/2011-12-link-patterns-spider-silk-melodies.html
>
> While these are the originating papers (
>
http://arxiv.org/ftp/arxiv/papers/1111/1111.5297.pdf [1]) and (
>
http://math.mit.edu/~dspivak/informatics/ologs--basic.pdf [2])
>
> It seems to me that the author is reinventing the
wheel (though with a nice
> twist re formulating / expressing o-logs and
"sketches").
>
> Especially since their review of the ontology
field (in the *
> ologs--basic.pdf* paper) seems to extend only to
RDF/OWL and completely
> ignores (or misses) work on Common Logic,
conceptual graphs and the most
> glaring omission - the work on category theory in
Bremen.
Incidentally,
> such an omission appears to be an unfortunate
corollary of the crowding out
> of any non-RDF/OWL work.
>
> In any event, it's interesting work, though the
correlation between the two
> seemingly disparate fields (spider silks and
melody) reminds me more of the
> seminal "Unreasonable Effectiveness of
Mathematics in the Natural Sciences"
> speech -
http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html [3]
>
> A lot of semantic mapping to date has indeed
focused on DL level mappings
> (cf Euzenat & Shvaiko's Ontology Matching
book [4]), but there is a rich
> set of logical mappings which can capture a lot
of these structural
> similarities between disparate fields. I know
I've repeated this claim
> before, but the limited expressivity of DL's
mutes many of these mappings,
> because well, they generally aren't captured
(can't be expressed) in the
> formalism. There is something to be said for
picking the correct language
> to describe a domain, where difficult problems
become much simpler. I
> suspect this will be one of the first major
obstacles in orchestrating
> services based on LOD sets beyond the low hanging
fruit currently being
> explored.
>
> In a previous discussion with Bijan, we were
talking past each other re
> reasoning over expressive ontologies. I kept on
talking about reasoning
> "off-line", while he insisted such
projects were fatally intractable. I
> later realized the disconnect was that I was
talking about verifying an
> expressive ontology (which you only need to do
once, hence off-line), while
> he was thinking that you need to process the entire
ontology for every
> query. Verification need be done only once (and
indeed, off-line), while
> the deployment of queries over fragments of the
ontology can then deploy
> more optimized tools.
>
> I think there's an attractive case for
articulating in some way, in some
> place, an expressive version of an ontology, even
if for certain services /
> tasks you only deploy a decidable fragment of
said ontology. For one, it
> can greatly facilitate semantic mappings, while
secondly, it makes the
> entire project more upwards compatible,
especially as the major DL's are
> continually adding greater expressivity. The
expressive version of the
> reference ontology can function a sort of road
map for deployment, a sort
> of technology agnostic commitment, whereas DL or
otherwise deployed
> artifacts are technology dependent products /
services...
>
> Lastly, I'd point out that the group at the University of Toronto does have
> a paper on this topic (modularizing and reducing
expressive ontologies into
> ontologies of other types that preserve the
logical structure of the
> models), which has the incidental benefit of
being able to identify logical
> similarity between theories according to an open
repository... I will see
> if I have permission to distribute a pre-print to
the list (Michael?).
>
> ===
> [1] Tristan Giesa, David I. Spivak and Markus J.
Buehler "Reoccurring
> Patterns in Hierarchical Protein Materials and
Music: The Power of
> Analogies" BioNanoScience Volume 1, Number
4, 153–161, DOI:
> 10.1007/s12668-011-0022-5
> [2] D.I. Spivak, R.E. Kent “Ologs: a
categorical framework for knowledge
> representation". PLoS ONE (in press):
e24274. (2011)
> doi:10.1371/journal.pone.0024274
> [3] Wigner, E. P. (1960). "The unreasonable
effectiveness of mathematics in
> the natural sciences. Richard courant lecture in
mathematical sciences
> delivered at New York University,
May 11, 1959". Communications on Pure and
> Applied Mathematics 13: 1–14.
doi:10.1002/cpa.3160130102.
> [4] Jérôme Euzenat, Pavel Shvaiko. *Ontology
Matching*. Springer-Verlag,
> Berlin Heidelberg (DE), 2007
>
> Best,
> Ali
>